Cálculo Ejemplos

$f (x) = \sin (\sqrt{\cos (\sqrt{1 - x^{2}})})$

Paso 1

Aplica reglas básicas de exponentes.

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Paso 1.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{1 - x^{2}}$ como ${(1 - x^{2})}^{\frac{1}{2}}$ .

$\frac{d}{d x} [\sin (\sqrt{\cos ({(1 - x^{2})}^{\frac{1}{2}})})]$

Paso 1.2

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{\cos ({(1 - x^{2})}^{\frac{1}{2}})}$ como ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

$\frac{d}{d x} [\sin ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})]$

Paso 2

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \sin (x)$ y $g (x) = {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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Paso 2.1

Para aplicar la regla de la cadena, establece $u_{1}$ como ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

$\frac{d}{d u_{1}} [\sin (u_{1})] \frac{d}{d x} [{\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}]$

Paso 2.2

La derivada de $\sin (u_{1})$ con respecto a $u_{1}$ es $\cos (u_{1})$ .

$\cos (u_{1}) \frac{d}{d x} [{\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}]$

Paso 2.3

Reemplaza todos los casos de $u_{1}$ con ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \frac{d}{d x} [{\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}]$

Paso 3

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = x^{\frac{1}{2}}$ y $g (x) = \cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

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Paso 3.1

Para aplicar la regla de la cadena, establece $u_{2}$ como $\cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{d}{d u_{2}} [{u_{2}}^{\frac{1}{2}}] \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 3.2

Diferencia con la regla de la potencia, que establece que $\frac{d}{d u_{2}} [{u_{2}}^{n}]$ es $n {u_{2}}^{n - 1}$ donde $n = \frac{1}{2}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {u_{2}}^{\frac{1}{2} - 1} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 3.3

Reemplaza todos los casos de $u_{2}$ con $\cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2} - 1} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 4

Para escribir $- 1$ como una fracción con un denominador común, multiplica por $\frac{2}{2}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 5

Combina $- 1$ y $\frac{2}{2}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 6

Combina los numeradores sobre el denominador común.

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1 - 1 \cdot 2}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 7

Simplifica el numerador.

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Paso 7.1

Multiplica $- 1$ por $2$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1 - 2}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 7.2

Resta $2$ de $1$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{- 1}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 8

Combina fracciones.

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Paso 8.1

Mueve el negativo al frente de la fracción.

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 8.2

Combina $\frac{1}{2}$ y ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{{\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}}}{2} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 8.3

Mueve ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}}$ al denominador mediante la regla del exponente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) (\frac{1}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})])$

Paso 8.4

Combina $\frac{1}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ y $\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [\cos ({(1 - x^{2})}^{\frac{1}{2}})]$

Paso 9

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \cos (x)$ y $g (x) = {(1 - x^{2})}^{\frac{1}{2}}$ .

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Paso 9.1

Para aplicar la regla de la cadena, establece $u_{3}$ como ${(1 - x^{2})}^{\frac{1}{2}}$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{d}{d u_{3}} [\cos (u_{3})] \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])$

Paso 9.2

La derivada de $\cos (u_{3})$ con respecto a $u_{3}$ es $- \sin (u_{3})$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (- \sin (u_{3}) \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])$

Paso 9.3

Reemplaza todos los casos de $u_{3}$ con ${(1 - x^{2})}^{\frac{1}{2}}$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (- \sin ({(1 - x^{2})}^{\frac{1}{2}}) \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])$

Paso 10

Combina $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ y $\sin ({(1 - x^{2})}^{\frac{1}{2}})$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}]$

Paso 11

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = x^{\frac{1}{2}}$ y $g (x) = 1 - x^{2}$ .

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Paso 11.1

Para aplicar la regla de la cadena, establece $u_{4}$ como $1 - x^{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{d}{d u_{4}} [{u_{4}}^{\frac{1}{2}}] \frac{d}{d x} [1 - x^{2}])$

Paso 11.2

Diferencia con la regla de la potencia, que establece que $\frac{d}{d u_{4}} [{u_{4}}^{n}]$ es $n {u_{4}}^{n - 1}$ donde $n = \frac{1}{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {u_{4}}^{\frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}])$

Paso 11.3

Reemplaza todos los casos de $u_{4}$ con $1 - x^{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}])$

Paso 12

Para escribir $- 1$ como una fracción con un denominador común, multiplica por $\frac{2}{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 13

Combina $- 1$ y $\frac{2}{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 14

Combina los numeradores sobre el denominador común.

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{1 - 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 15

Simplifica el numerador.

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Paso 15.1

Multiplica $- 1$ por $2$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{1 - 2}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 15.2

Resta $2$ de $1$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{\frac{- 1}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 16

Combina fracciones.

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Paso 16.1

Mueve el negativo al frente de la fracción.

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {(1 - x^{2})}^{- \frac{1}{2}} \frac{d}{d x} [1 - x^{2}])$

Paso 16.2

Combina $\frac{1}{2}$ y ${(1 - x^{2})}^{- \frac{1}{2}}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{{(1 - x^{2})}^{- \frac{1}{2}}}{2} \frac{d}{d x} [1 - x^{2}])$

Paso 16.3

Mueve ${(1 - x^{2})}^{- \frac{1}{2}}$ al denominador mediante la regla del exponente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2 {(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [1 - x^{2}])$

Paso 16.4

Multiplica $\frac{1}{2 {(1 - x^{2})}^{\frac{1}{2}}}$ por $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {(1 - x^{2})}^{\frac{1}{2}} (2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})} \frac{d}{d x} [1 - x^{2}]$

Paso 16.5

Multiplica $2$ por $2$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [1 - x^{2}]$

Paso 17

Según la regla de la suma, la derivada de $1 - x^{2}$ con respecto a $x$ es $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

Paso 18

Como $1$ es constante con respecto a $x$ , la derivada de $1$ con respecto a $x$ es $0$ .

Paso 19

Suma $0$ y $\frac{d}{d x} [- x^{2}]$ .

Paso 20

Como $- 1$ es constante con respecto a $x$ , la derivada de $- x^{2}$ con respecto a $x$ es $- \frac{d}{d x} [x^{2}]$ .

Paso 21

Multiplica.

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Paso 21.1

Multiplica $- 1$ por $- 1$ .

$1 \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [x^{2}]$

Paso 21.2

Multiplica $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ por $1$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [x^{2}]$

Paso 22

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 2$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (2 x)$

Paso 23

Simplifica los términos.

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Paso 23.1

Combina $2$ y $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}))}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} x$

Paso 23.2

Combina $\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}))}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ y $x$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})) x}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Paso 23.3

Factoriza $2$ de $2 \cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Paso 24

Cancela los factores comunes.

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Paso 24.1

Factoriza $2$ de $4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{2 (2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}$

Paso 24.2

Cancela el factor común.

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{2 (2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}$

Paso 24.3

Reescribe la expresión.

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x}{2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Paso 25

Reordena los términos.

$\frac{x \cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}} {(1 - x^{2})}^{\frac{1}{2}}}$